Epistemology, Cognition and Category Theory: An Overview

Lately, I’ve been working on learning skateboarding and some tricking.
At the moment, I’m pretty terrible at both. If I had the time to
practice more, I would improve very quickly. Especially if I had
someone better to practice with who could teach me and push me
harder. It’s amazing how the presence of others can stimulate
improvement, especially when they are significantly more proficient at
what you’re trying to learn.

Of course, after about fifteen minutes of backflips and ollies, my
mind is thrust into philosophic overdrive. Typical.

Phenomenology - The Study of Me.

A few ideas have been tumbling around in my head lately and I’m more
able to clearly conceptualize certain problems that eluded me before.
There seems to be a universal means of modeling ideas, activities and
problems that leads me to learn faster. I want to describe how I’ve
modeled skateboarding and tricking using category theory as an in
depth example – and to exhibit some math ideas I’ve been playing
around with. Many people find that the more you learn, the faster you
learn new things. I agree, but additionally, I’ve found that
conceptualizing the mind both helps me to learn faster and to identify
activities to strengthen specific mental faculties.

I love learning new things. I get to experience beginner’s mind again
and it gives me a chance to reflect on the process I use to learn. By
actively observing beginner’s mind, you can refamiliarize yourself
with its nature, so that you might be able to partially apply this
state of mind when you need it. By introspecting on this process, I
hope to continually improve it. I try to approach new activities and
skills from a multitude of perspectives and I like to examine the
similarities between everything.

Developing Versatility

Lately, I’ve taken some time off from pondering the finer mysteries of
life to examine closer the structure of cognition and knowledge itself
in an attempt to discover for myself a more generalized model of
cognition. As our world accelerates towards convergence, it’s
becoming ever more important for us to consume information and acquire
knowledge faster. In a world perilously close to technocracy, where
it’s likely that we soon won’t have a need for much of today’s labor
force, those who aren’t able to keep up will find themselves
disillusioned and searching for meaning. That’s not to say that
everyone needs to be a quantum physicist, but we’ll all be dealing
with rapid change.

Technological development continues to outdate itself faster and
faster. Those who commit themselves today in service of a static
vision of the future will find out tomorrow that they’ve oblidged
themselves to a future past. New technologies will continue to
cannibalize the demand for outmoded tech and apps. Revenue streams
which could traditionally be depended on for decades, we can now only
count on for the next quarters. Those who are networked and in touch
with the right information at the right time will be nimble enough to
forward their chips to the next big players. Luckily, risk for
technology investments do not systemically affect the entire system in
the same way as the housing market.

The rest of us? Plebs. Don’t get me wrong, we’ll have great quality of
life, but still we’ll likely be peasants, without much significance in
our lives, except that which we create. Those of us who continue to
diversify through extensive learning will find their skillsets
versatile enough to remain in demand throughout our unpredictable,
turbulent journey of convergence.

We’re pretty much living out The Matrix. With Wikipedia, we’re two
steps away from downloading the history of Eastern Civilization or
Kung Fu. As the nodes in our social network converge toward
super-connected, as the speed of communication exponentially
increases, so does the rate and amount of information we share.
Additionally, the way we share knowledge adapts to this new bandwidth
because we also share tools to learn and teach more efficiently. So
then, we learn to consume information and acquire knowledge more
rapidly. Systems evolve, new tech is created, science is
revolutionized and new culture is produced – these all create new
things for people to learn.

It’s interesting that, while in the next few decades there will be
immensely increased demand for knowledge and versatility, shortly
after that, there may be be little to none, as artificial intelligence
begins to supplant almost all of our responsibilities and jobs. It’s
at this time that we need to push ourselves even harder, if we hope to
be capable of taming out-of-control technology.

A Universal System for Conceptualizing Anything

So learning about how to learn seems reasonable. A lot of people have
trouble learning new things because they lack multifaceted mental
tools to quickly and sufficiently model what they’re trying to learn.
So we need a universal system of modeling any problem. Yet, modeling
the knowledge and skills to acquire is not enough. We also need to be
able to envision a model of the mind which allows us to optimize its
capabilities. And a robust process for conceptualizing anything,
should also be capable of modeling our mind.

Understanding category theory is fundamental to a universal system of
modeling problems because it’s flexible enough to provide the
foundation for a universal language of high level math. It sounds
complicated, but it’s really not. It’s a shame that most people don’t
make it far enough in math to learn about this. And I’m only vaguely
familiar with it.

A Brief Journey to the Metaverse

Why could the underlying language of math be used to robustly
conceptualize anything? To justify, it’s time for a brief interlude
into the nature of the metaphysical. When I refer to information, I
mean it as the instances of knowledge that people typically consume,
both in life and on the internet, including tweets, news articles,
baseball stats, and stories about friends. Bits of information are
like real-world manifestations of bits of knowledge that people can
directly consume to internalize into their personal knowledge.

Each person has constructed their own internalized system of knowledge
representing their understanding of how things work and of all things
relationships to all other things. You can begin to group together
people along certain dimensions to see how each person’s internalized
system of knowledge overlaps with others in their own group, as well
as with that of other groups. These dimensions include groupings by
geography, culture, family, religion, education, time and many
groupings that are more complicated. Someone’s internalized knowledge
of the world can be affected by skewed perspective and will include
information that is false, inaccurate, oxymoronic, incomplete,
undefined or irrationally constructed.

Each person also constructs their understanding of the knowledge of
each other person they know, at least to some extent. To greatly
complicate the scope of the problem, this knowledge about others’
knowledge is also constructed to form generalizations for the
groupings listed above. Not only that, but it’s also recursively
reflective – I know that you know that I know that you know … etc.
Sometimes considering this reflective information seems incredibly
over-analytical, possibly paranoid and just silly. However, there’s
many inferences that you couldn’t deduce otherwise, though it’s
important not to weight it with much priority.

If you make some important limitations on this extremely complicated
system, like cutting off recursive reflection as well as a few others,
then you’ll find that the number of nodes and edge’s in this graph is
finite – though it quickly approaches astronomical proportions. A
googolplex? No, think
higher – like
Graham’s Number.
It’s crucial to note that it is finite. No person or computer could
ever model or process all of this information. The
computational capcity of the universe
is not nearly enough. And we’re just considering the complete graph,
including ‘null’ nodes, of one person’s internalized system of
knowledge, which includes the dimensional groupings listed above along
with a limited number of reflections. It’s important to note that
this impossibly large graph is a model that includes nodes accounting
for the effect of information that person has not actually stored.

The problem space can be significantly compressed. For example, if
you only account for the information stored in that person’s brain,
this compresses the size of the graph. However, it doesn’t allow you
to construct valid products of the internalized knowledge of multiple
people. Other aspects are sacrificed by only considering information
stored in hardware. More effectively, you can compress by reducing
and generalizing the forms of these pieces of knowledge. You’ll have
to forgive me. This is tough to conceptualize and I know that much of
what I’m saying is not as coherent as it should be, but I’m
visualizing this and while it makes a lot of sense to me, it’s really
tough to convey.

Universal Knowledge, the Best Kind

In our future world, we’re going to have to familiarize ourselves with
lots of manmade systems of knowledge. For example, Cisco releases a
new IOS, network technicians gotta learn about it. Apple releases a
new OSX, developers gotta learn it. Google releases new features on
Analytics, marketing’s gotta know it. But none of this is really
… universal. In fact, as a software developer, I’ve gotta say, it’s
pretty fucking annoying.

“That’s just a waste of neurons.” - Bernie Cossell, owner of the
eighth email address and my Unix teacher.

On the other hand, mathematics very definitely is universal. Science
is a bit flakier. It tries to represent itself as universal
knowledge, continually purging itself of any inaccuracies and
propagating the updated system to its devotees. This is eerily
similar to how a religion operates. So, how does science differ from
math in this degree? It’s a system that tries to map as closely as
possible to universal knowledge, but can sometimes contain false or
irrational elements, whereas math is pure universal truth. It has
always existed metaphysically in it’s current and final form since the
inception of the universe – by the way, this means it exists outside
of time. There are few other fields that can make this claim.
Perhaps some of philosophy, particularly logic.

All universally shared metaphysical entities must only be true.

Math is literally universal – fucking space aliens will learn the
exact same math we learn. Perhaps their system of math will have a
cultural overlay that maps differently. Different notation and extent
of knowledge. But it represents the exact same invisible metaphysical
structures that must certainly be true. So if we needed tools to
robustly model knowledge itself, perhaps we should base it on a
completely solid foundation. Yes, every person has their own different
and incomplete conception of math, but they all definitely map to the
same universal structure, whereas the metaphysical structure of other
forms of knowledge is exceedingly fragmented.

The only other universal system of knowledge I know of is GNU and
Linux, lulz.

Category theory is [part of] the underlying language of higher level
math. If this metaphysical kernel of math can be used to model the
rest of such a pure form of information, wouldn’t it be useful in
modeling the rest of our knowledge. And interestingly, though math is
pure truth, it can be used to model systems that include false &
indefinite information.

-1/12 = 1 + 2 + 3 + 4 + 5 + … No, really. It’s true.

Most people’s extent of conceptualizing a problem space ends with
tree-like structures, sets and graphs. I mean like graph theory
graphs. Most people don’t understand that they mentally model things
this way. It’s moreso done subconsciously. And these are fairly
powerful, but come up woefully short when trying to intellectually
understand things like social interaction, artificial intelligence,
learning and cognition, which aren’t usually considered ‘mathematic.’

Modeling Social Interaction

For social interaction, if you try to model this using trees and
graphs, your behavior is going to be limited and very repetitive – if
your interacting on an intellectual basis. Of course, most people
don’t think of it this way. They just interact using subconscious
behaviors, which are learned over a long time. But if this stuff
doesn’t come naturally to you, then you won’t experiment socially on a
cognitive level. So you need a different means of understanding
things.

With category theory, you can conceptualize interactions as functions
passed from person to person. You can observe specific behaviors,
then form ideas about behavior types and patterns. You do this by
parameterizing specific behaviors that you observe and imitating them,
observing the effects under various conditions and reasoning about
cause and effect to optimize your own behaviors.

What do I mean by parameterizing behaviors? For the specific behavior,
“John bought a drink for his friend,” you can observe the behavior as
a function. Then, you can first parameterize the subject as a
variable: “[X] bought a drink for his friend.” So now you can consider
the action if performed by yourself or someone else. Then you can
parameterize the direct and indirect objects to arrive at an even more
meta function: “[X] bought [Y] for [Z].” You can also parameterize the
verb: “[X] [V] [Y] for [Z].”

This may sound overanalytical and superfluous, but it’s very powerful
because you’ve now arrived at a sort of ‘form’ for a specific ‘kind’
of human behavior. You can build up a vocabulary of these ‘kinds’ of
human behavior and recombine them in order to model and emulate nearly
any behavior. And because these kinds of behavior are much more
generic, there are markedly fewer to know. And the combinations of
base forms could be finite, depending on what you consider as a base
form.

So you can take the original form with “Even though [A],” to conjoin
them into the new behavior “Jerry bought a drink for a homeless guy,
even though we told him not to.” This is kind of a high-level
overview of how to use category theory to model something, but I
didn’t cover monads. In this case, monads are the functions you would
use to combine the forms. Additionally, you need to pass in functions
that describe how those forms are combined. You can also weave
together semantics with the substituted forms, along with
optimization, dependency and objectives, for an attempt at autonomous
behavior.

It gets a little complicated, but the point is – with category
theory, you can recombine bits and pieces of conceptual structure and
functionality to arrive at an accurate model of anything. You can get
further and further meta with it, to become more adaptive. As you
parameterize behaviors you observe and construct behavior-kinds (kind
is a concept used in the programming language Haskell btw), then you
can partially fixate these behavior-kinds with some of their
parameters. At this point, you can begin to compare the similarity of
kinds of behavior in various situations. I.E. What would it mean,
semantically, if “John bought a drink for [X].” is applied using the
various direct objects: his friend, his ex, and a homeless guy. I
don’t mean semantically in the sense of the meaning of words. Rather,
the meaning of the actions, as perceived by various people. It’s the
same type of behavior, and while it has different meaning as applied
in different situation, there are also similarities that can be
observed and reflected on.

You can even construct these models inside of a kind of cyclic monadic
function, so you can acquire behaviors as you observe them, construct
the next step’s behavior by recombining existing behaviors and pass
acquired information to the next step. I’m sure there’s math terms
for most of what I’m describing, but I don’t know what they are. This
cyclic function that I’m describing has been particularly interesting
to me recently.

I’ll briefly overview the various faculties of the brain and the mind
and explain how they can be combined. By training various activities
and subjects, we can focus on improving specific functions of the
mind. I’ll list some examples, briefly explaining how each one
coordinates various functions of the mind.